### Abstract

We study the impact of the QCD Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution on the geometric scaling of gluon distributions that is expected to hold at small x within the saturation models. With this aim we solve the DGLAP evolution equations with the initial conditions provided along the critical line Q^{2}=Q_{s}^{2}(x) with Q_{s}^{2}(x)∼x^{-λ} and satisfying geometric scaling. Both fixed and running coupling cases are studied. We show that in the fixed coupling case the geometric scaling at low x is stable against the DGLAP evolution for sufficiently large values of the parameter λ, and in the double logarithmic approximation of the DGLAP evolution this happens for λ≥4N_{c}α_{s}/π. In the running coupling case geometric scaling is found to be approximately preserved at very small x. The residual geometric scaling violation in this case can be approximately factored out and the corresponding form factor controlling this violation is found.

Original language | English (US) |
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Article number | 014013 |

Pages (from-to) | 140131-140139 |

Number of pages | 9 |

Journal | Physical Review D - Particles, Fields, Gravitation and Cosmology |

Volume | 66 |

Issue number | 1 II |

State | Published - Jul 1 2002 |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics
- Physics and Astronomy (miscellaneous)

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## Cite this

*Physical Review D - Particles, Fields, Gravitation and Cosmology*,

*66*(1 II), 140131-140139. [014013].